20. On the Solution of Nonlinear Algebraic Equations Following Periodic Forced Response Analysis of Nonlinear Structures Using Different Nonlinear Solvers

In periodic forced response analysis of nonlinear structures, most of the time analytical solutions cannot be obtained due to the complex behavior of the nonlinearity and/or due to the number of nonlinear equations to be solved. Therefore, numerical methods are widely used. For periodic forced response analysis of nonlinear systems, generally Harmonic Balance Method (HBM) or Describing Function Method (DFM), which transform the nonlinear differential equations into a set of nonlinear algebraic equations, are used. In the literature, there exist several nonlinear algebraic equation solvers based on Newton’s method which have different convergence properties and computational expense. In this paper, comparison of computational performance of different nonlinear algebraic equation solvers are studied where, solvers with different convergence order are selected based on the number of Jacobian matrix and vector function evaluations. In order to compare the performance of these selected nonlinear solvers, a lumped parameter model with cubic stiffness nonlinearity is considered. Several case studies are performed and nonlinear solvers are compared to each other in terms of solution time based on error tolerance used.